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ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

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##### A can complete a workpiece in 12 days. B requires 18 days to finish the same workpiece, whereas C can do it in 24 days. All three of them started working on the same workpiece, but due to some reason, C left work after working for 3 days with A and B. What should be the overall time taken to complete this workpiece ?
 1) 5-3/10 days 2) 6-7/10 days 3) 6-3/10 days 4) 7-3/10 days 5) None of these
Explanation : A,B and C altogether work for 3 days = 3 (1/12+1/18+1/24) = 13/24 parts
So, remaining (1-13/24) = 11/24 parts
B and C can do in 1 day (1/12+1/18) = 5/36 parts
Now, B & C can do this in (11/24 )/(5/36) = 33/10 days = 3-3/10 days
So, overall time taken to complete this workpiece =  6-3/10 days

##### A is 25% more efficient than B and 50% more efficient than  C. A and B together can complete a work in 20 days. How many days the same work  can be completed by B and C if both work  in alternate days and B starts  the work  first  ?
 1) 48 days 2) 49 days 3) 50 days 4) 51 days 5) None of these
##### Alok takes 8 more days than Bikas to finish a work. Alok and Bikas start the work and Bikas leaves the task 9 days before the work is finished. If Alok completes 75% of the overall work, how long would Alok have taken to finish the work if he had worked independently?
 1) 8 days 2) 10 days 3) 12 days 4) 14 days 5) None of these
Explanation : Let, Bikas takes x days to finish the work . So, Alok would take (x +8) days to finish the same work.
Given, Alok finishes 75% and Bikas finishes 25% work respectively.
So, (x+8)3/4 = (x/4)+9
or (3x+24)/4 = (x+36)/4
or 2x = 12
or x = 6

Therefore, Alok would finishes the work (6+8) = 14 days alone.

##### A fort has provisions for 250 soldiers for 35 days. After 5 days a reinforcements of 25 soldiers were arrived. Again after 10 days, 25 soldiers left the fort. How long will the remaining provisions lasting ?
 1) 12 2) 16 3) 18 4) 19 5) None of these
Explanation :
Short- Cut Methods:

ND (No. of days) = N1D1 + N2D2 = total amount of food after 5 days.
or ( 250 X 30) = ( 250 + 25) X 10 + 250 X x
or  x = 19 days .
##### Seven men and four boys can complete a work in 6 days. A man completes the double work than a boy. In how many days will 5 men and 4 boys complete the work ?
 1) 4 2) 5 3) 6 4) 8 5) None of these
##### Three men or eight boys can do a piece of work in 17 days. How many days will two men and six boys together take to finish the same work ?
 1) 9 days 2) 11 days 3) 14 days 4) 12 days 5) None of these
Explanation :
3 men = 8 boys
2 m = (8/3)x2 =  16/3 boys.
(2 men + 6 boys) = (16/2)+6 boys =  34/3boys
8 boys can complete the work in 17 days
or 34/3boys boys can complete the work in x days
or (34/3) : 8 = 17 : x
or x =(17x8x3)/34  = 12 days
##### 10 man can finish a piece of work in 15 days. 8 women can finish the same work in 25 days. Only 10 women started working and in a few days completed a certain amount of work. After that 3 men joined them. The remaining work was completed by 10 women and 3 men together in 5 days . After how many did 3 men join with 10 women ?
 1) 11 2) 13 3) 15 4) 10 5) None of these
##### 16 men can complete a piece of work in 8 days. 20 women take 16 days to complete the same piece of work. 12 men and 10 women work together for 6 days. How many more days would 10 women alone require to complete the remaining piece of work ?
 1) 6 days 2) 8 days 3) 10 days 4) 12 days 5) None of these
Explanation : Given,16 men can complete a piece of work in 8 days while  20 women take 16 days to complete the same piece of work.
The ratio of  the capacity of doing work i.e. men to women = (20 x 16 ) : (16 x 8) = 5:2
So, 1 man = 2.5 women
Now, 12m + 10w = (12 x 2.5) = 40w
Given, 20 women take 16 days to complete the same piece of work.
1 woman can do it in = 16 x 20 = 320 days i.e. 1/320 parts in 1 day.
40 women can do in 6 days = (1/320) x 40 x 6 = 6/8 = 3/4 parts
Therefore, remaining 1-3/4=1/4 part of the work done by only 10 women in =
Applying Chain Rule:
M1 x D1 x W2 = M2 x D2 x W1
or 20w x16 x 1/4 = 10w x D2 x 1
or D2  = 8 days

##### A,B,C can do a  work in 36,54 and 72 days respectively.They started work together but A and B left the work 8 and 12 days before completion of the work respectively. Find the total number of days which the work has been completed ?
 1) 15 2) 18 3) 24 4) 30 5) None of these
Explanation : Let,the total numbers of days requires to finish the job is x days.
So, A works for ( x-8) days and B works for (x-12) and C works for x days.
Therefore,